The primary aim of this trial is to assess the net clinical benefit of 3-4 years of low-dose warfarin in the secondary prevention of idiopathic venous thromboembolism. The trial has been designed to test a safe and efficacious warfarin regimen which, after initial titration, will require infrequent outpatient blood or laboratory monitoring and thus will appeal to clinicians and patients currently reluctant to use long-term warfarin for secondary prevention. The trial will also evaluate participants with and without factor V Leiden, a recently described common inherited defect of anticoagulation which results in activated protein C resistance and increased risk of recurrent thrombosis.